My daughters age 14 and 16 are generally friendly and loving towards each other. The youngest daughter refuses to participate in family events that are important to everyone but her. For example, she refused to attend her sister's birthday dinner and her all state chorus performance stating she doesn't like the food chosen, or the music selections. We've stressed the importance of attending for other person as the "right thing to do." She says we're wrong and she shouldn't be made to attend something she doesn't want to. She is hurting those she loves and doesn't seem to care.
This situation happens a lot among teens. Be thankful you don't have three which puts one in the middle all the time! With two girls, the issues are usually competition, friends, independence, and control issues. I have to be general because the girls temperaments play a big role in the "why" question, the "what" question is much easier. It is a family decision (rule) to support the other girls activities, regardless of the excuses. If you sit the whole family down and hash out the rules that guide your family life, then everyone will have had a say and the conversation will acknowledge that you care what each person thinks. Some families do not prioritize this as being a total "rule" but a general guideline. Most families do want 100% participation and that will definitely effect both girls social lives. You need to have more than one conversation about this, and you and your spouse need to totally agree that you insist on (except for emergencies) support at all times.
It is your call - you are still in charge of the household but give teens as much opportunity as possible to discuss it ahead of time so the rules are clear and when an event comes up everyone knows what to do and how to behave.